Quizlets for tuesday, may 4, 1999

1) a) find   <p> for all states n > 1

     b) explain why, on physics grounds, the answer that you obtained mathematically
	in part (a) was entirely expectable

	(hint #1: what is the (experimental) definition of an expectation value?)
	(hint #2: what type of quantity is momentum?)

2) find   <x>   for all states n > 1

3) find   <U>   (U is the potential energy inside the box)

4) a) write down the energy operator

    b) find   <E>  (E is the total energy) for all states n > 1

    c) does the value of <E> match the energies calculated from Schroedinger's
	equation?

5) find   <x2> for all states n > 1

6) find   <p2> for all states n > 1   (hmmm… have you done this already?)

7) find the position where the particle is mostly likely to be found (for all states n > 1)

8) find the momentum at which the particle is mostly likely to be found

9) a) find the value of   x p   for all states n > 1

    b) does this satisfy the uncertainty principle?

10) what are the classical (macroscopic) expectations for the particle-in-the-box wavefunctions (as a function of position) and energies?  (for the wavefunctions, you should be able to specify the probability density values as a function of x precisely; for the energies, you should be able to describe how they are different than those given by the Schroedinger equation)

11) take the limit (as n     ) of the particle-in-the-box wavefunctions and energy level values and show that they indeed have the properties you described in the previous question